A leisure vehicle, for example, an ATV, typically runs with wheels on the ground through various conditions, such as sandy soil. In such cases, the ATV is more likely to start and accelerate on the sandy soil. Since a grip force between the wheels and a ground surface of the sandy soil is small, it is in many cases difficult to start or accelerate the vehicle without occurrence of a substantial slip. If a large drive force (rotational torque) is applied to a drive wheel during a start or during acceleration, the drive wheel tends to slip, making it difficult to achieve a smooth start or smooth acceleration. In such situations, a driver of the vehicle is required to manipulate an accelerator of the vehicle to cause a power unit such as an engine to drive the wheel with a small drive force (drive torque) during the start and to gradually increase the drive force after the start. During the acceleration of the vehicle, such manipulation of the accelerator is required to inhibit a substantial slip as well. Such a situation takes place when the vehicle is running on roads such as a snowy road, a muddy road, a wet road, and so on, because the grip force between the wheels and their ground surfaces is small (Publication of Japanese Examined Utility Model Application No. Hei. 5-9562).